this is really bad poker and you should know this by now.

You're assuming that your opponents are rational at this point. If they're check-calling, their range is a type of BS. I expect to get called and see two pair sometimes, for example. ("I thought you had AK.")

From the point of view of playing towards GTO, sure. But while I appreciate GTO strategies and concepts as a foundation to build on, I don't think they're as profitable as more exploitative concepts when applied to lower level games. "Bad poker" can be more profitable than "good poker" if you've defined good and bad in certain ways.

Seriously man, for someone that makes so many assertions and asks so many questions, you certainly do more than your fair share of question dodging.

Put em on a river range for calling please because this:

Just doesn't answer the question at all. There is most certainly a correct river check calling range for this spot. Figure out how you think this differs from the opponent's actual check calling range and look for exploits.

Your proposed strategy is neither gto nor exploitive. It's just bad.

You're right that it doesn't answer your question. But it addresses the general situation.

Even in how you frame the question, you're assuming that the opponent's range is stratified. For example, I would expect to see QT check-raise me *AND* I would expect to see QT call me. I don't know what a generic opponent is going to do with that hand. There's a lot of variation between opponents and both outcomes are totally "reasonable" (understood as your opponent's logic). And so constructing a rigid range as if that's actually a decent model of what the opponent is doing isn't necessarily going to be a good way to figure out how to play this spot.

You're making an error assuming that the correct play is nothing but a minor pertubation from some sort of idealized GTO-like solution.

If you agree that there isn't actually a bluff 3-betting hand for reasons, then it's feasible that there isn't actually a bet-fold range for reasons. And for the same reasons I think it's dumb to force a bluff 3-betting range, I think it's dumb to force a bet-folding range.

When the pot is large, you need to get to showdown more often. While it's probably not "perfect" to get to showdown 100% of the time, if picking a hand range to bet-fold means I go to showdown only 90% of the time when I should getting there 98% of the time, I'd rather make the mistake of getting to showdown 100% of the time than 90% of the time.

There are some mistakes I'd rather make than others. If you want to bet-fold KJ and 3-bet bluff AJ, go for it. It's your money.

More dodging. Peace.

While Bob throws a temper tantrum because I refuse to play his game, I'm going to finish explaining why I'm distrustful of assuming a GTO starting point in places like this where there is a significant variation in the range of possible strategies your opponent could be using.

The general assumption of GTO is that your ranges are both continuous and stratified. Something like this:

* With the lowest x% of your range, you should check-fold
* With the next y% of your range, you should check-raise-bluff
* With the next z% of your range, you should check-call
* Etc.

Graphically, it looks something like this:

But reality looks more like this:

(These hash marks don't represent 100% of the time. It could be 30% or 80%. The point is that the truest model of your opponent *IS* a weird BS range.)

So drawing the line at one particular hand as a way to model what opponents are doing is simply starting from a false assumption. And so the conclusions are going to be equally weak.

Furthermore, this is not about making minor perturbations from a GTO-like strategy. These are very significant deviations. At this point, GTO-like is at best a heuristic, just like all of the other heuristics we have. The variations are greater than the accuracy of the assumptions that are being put into the calculations.

Hand ranges are helpful for determining where you stand relative to your opponent in terms of hand strength. But drawing rigid lines and assuming that you can fit your opponent into a box is going to cause some significant errors.

So I'm rejecting the hypothesis. If that's dodging the question, so be it. I'm not going to waste my time with a detailed analysis from a starting point that I think is incredibly flawed. It's one thing to have an overall hand range (going into the river, he has these hands). It's quite another thing to take that list, order them from weakest to strongest, and start drawing GTO lines through the range as if that's what your opponent is doing.

(Especially when Bob has already admitted that he's just kind of spitballing his own divisions and has not presented a single hand range of his own.)

Here are the key features I see in this hand:
1) The Q helps villain's hand range much more than it helps ours. This puts upward pressure on our value betting range, raising the floor of where we should even begin to do that.
2) The pot is quite large when facing a check-raise, so I'm going to want to get to showdown a lot. This puts downward pressure on the size of the bet-folding range.

I wouldn't be surprised to discover that in a deep analysis, you're only bet-folding a couple combos of a single hand type. You shouldn't be bet-folding too many hands on the river to begin with, and with these two statements being true, you should be doing it even less.

If I miss a theoretical tenth of a big bet because I don't bet-fold AJ here, I'm not going to lose sleep over it.

You can input hands at frequency in solvers.

I don't think anyone said you couldn't.

Let's say that the quality of your measuring device is +-0.1. You measure two collections of objects and calculate the average. One collection has an average that is 0.01 greater than the other. You cannot conclude with *any* confidence that one collection is on average greater than the other. It's all within the noise.

Unless there's some reason that's presented for me to think otherwise, in this spot, trying to parse the bet/fold line is simply within the noise. There's not enough information out there to come to a solid conclusion about it. So trying to argue that failing to bet/fold any hands at all is simply "bad poker" is just a terrible way to assess the situation. All I've done is take those bet-fold hands that are within the noise and either moved them to check-behind or bet-call. Since it's all in the noise anyway, it literally doesn't matter.

I don't think I need to force myself to bet-fold anything here. I don't think the math (when taken at the high level) justifies that it's necessary.

The way you can disprove me is to come up with some examples, post the assumptions and results, and show me that in a variety of cases, there's a significant bet-fold range in this spot (obviously including information about our hand range given the preflop 3-bet, flop, and turn bets) and that they're all basically the same types of hands. You're free to vary villain's ranges within reasonable bounds.

Edit: In economics, the concept in play is elasticity: How much do supply/demand change when the price changes? I'm drawing a type of parallel to that here. If you can show me that the ranges are fairly stable under a wide range of assumptions, then it becomes really important to play within those bounds. If the ranges are unstable under a wide range of assumptions, then it makes no sense to be dogmatic about what to do in that situation.

Then why do we estimate at all?

If you can't figure that one out, it's not really my problem. But this question does show me that you prefer dogmatism to reasonable discussion.

If there’s so much noise in our estimation of ranges then why do we even discuss poker strategies?

Again, if you can't figure it out, it's not my problem. My position has been stated clearly.

I've even outlined both a practical and theoretical foundation for you to directly challenge my perspective for this hand. Literally, it's a framework for you to directly prove me wrong. But it seems you've chosen to ignore that and hold onto something that either demonstrates a lack of reading comprehension or pure obstinance.

So go ahead and be dogmatic. Your counter-argument so far is not any better than dead.money arguing that he can exploit anyone who bet-folds ever, except in the opposite direction.

I don't need that to know that the combination of these adjustments:

-never bluffing this turncard

-bet calling your entire river betting range

is the wrong way to go for any serious player. If you eliminate bluffs, then you should also expand your value range. You choose to eliminate bluffs and tighten your value range. This is inconsistent with the reads given.

----

You can reject the indifference principle if you want. I don't.

Since our turn strategies are very different, then we will never agree on river strategy. However, if anyone else is still reading, here's what I think of the river situation:

button river bluffing frequency: 12.1212%

button river bet fold frequency: 21.7%

subtract one from the other = 9.6% = the % of the river betting range that is bet folded for value, rounded off of course.

One could make the argument here that we're never going to get the frequencies right. I don't dispute this. However, I do think that in the modern poker environment it's important to have a strategy that is consistent with the indifference principle. Without it we would have no default strategy from which to deviate; we would end up making adjustments that contradict each other such as Aaron's turn bluff elimination and river checking range expansion.

If instead we can identify where the margins would be vs strong players, we can correctly exploit vs poor players. By adjusting exclusively near the margins, we also put a limit on the exploitability of our strategy.

Don't take it from me though. Maybe take it from Matt Hawrilenko:

From The Intelligent Poker Player by Phil Newall page 115.

What are your assumptions here?

Also, the fact that you're holding these down to the first decimal point still shows me that you've either not comprehended or internalized the point I made about the quality of the input vs. the quality of the output. You've not shown whether these values are elastic or inelastic with respect to your input quantities.

There's some irony in the fact that you were willing to play the "Well, since we're here" game before, but now you're pulling back from that. More ironically, my point about things falling within the noise is *EXACTLY* what it means to be near the margins.

First, you're conflating two decisions on two different streets that as a single decision, and the second is highly dependent upon the specific card that fell and the specific circumstances that it created.

Also, I continue to assert that you're imposing structures into the noise. The removal of KQ from the turn bluffing range is literally one combination of hands that I've flipped. On the river, I've probably flipped one to two hands (since the other hand has been eliminated from the set of hands I have there).

So as much as you want to say that it's absolutely a terrible thing I'm doing, we're perhaps as little as two hands different from each other on these decisions. That it might be a relatively high percentage (because our ranges or small) is merely an illusion that results from your holding more tightly to your conclusions than the input data warrants.

At least check (and maybe you've fixed this in your head, but maybe not), you were giving the reads for the player that had already folded the flop.

Talking about the big blind.

Not really. I'm saying that since you never bluff the turn, you have no potential bluffs on the river. Thus your river betting range is exclusively (value) on every river card, which is very vulnerable. That is unless you think it's good to bluff the river with turn value hands; I don't think that's good.

That the indifference principle works like this:

In order to make the big blind indifferent to calling or folding hands that can only beat a bluff, the button should make his bluffing odds equal to the odds that the big blind is getting on a call. 7.25:1 = 1/8.25 = 12.121212% bluffing frequency.

In order to make the big blind indifferent to check raise bluffing or folding, the button should make his calling odds equal to the odds that the big blind is getting on a bluff. 7.25:2 = 2/9.25 = 21.62% folding frequency.

Since we're most definitely correct to fold our bluffs vs a check raise, the leftover %, or 9.6% is the fraction of our river betting range that should be value bet fold hands.

That's fine. I don't mind "being vulnerable" on the river when I have a small hand range that's very strong going in against a hand range that's nontrivially weaker than mine on average.

If the hand ranges were more equal going into the river, your point would carry more weight.

You're also ignoring much of what I'm posting. Shall I accuse you of dodging?

How many hands are in your range by the time you get to the river? What is *actually* being represented by the numbers?

Edit: I don't recall originally reading you explaining that you were just applying indifference at this point, as opposed to using a solver or other theoretical tool. My apologies if I totally glossed over that statement on the post I responded to.

If I missed a question then I apologize. If I don't address a paragraph then I either agree completely or I feel it's irrelevant to moving forward in the analysis.

Usually, it's the former. Much less often it is the latter; irrelevant points lead to useless tangents that we don't need to get into since we're already hogging the thread.

If you bluffed the turn more, then the ranges would be more equal going into the river. You've created this narrow range vs wide range situation without just cause by never bluffing this turncard on a one paragraph read from the op. This is indicative of a loss of value on the turn and river; there's also potential for previous street exploitation by the big blind whose bluffcatchers and weak draws get to showdown for much cheaper than they should.

About 105 value combos + assorted diamond draws.

Let's say you've got 110 hands on the river. According to your calculation, you should be bet-folding 9.6% of those, which is about 10.6 hands. That's less than one hand type. (Unpaired hand type = 16 combos.)

How much of an impact do you think it has on your EV if you changed your strategy from bet-fold to bet-call or check-behind with one hand type?